DLMF:18.28.E19 (Q5994)

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Language	Label	Description	Also known as
English	DLMF:18.28.E19	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle R_{n}(x)=R_{n}\left(x;\alpha,\beta,\gamma,\delta% \,|\,q\right)=\sum_{\ell=0}^{n}\frac{q^{\ell}\left(q^{-n},\alpha\beta q^{n+1};% q\right)_{\ell}}{\left(\alpha q,\beta\delta q,\gamma q,q;q\right)_{\ell}}\*% \prod_{j=0}^{\ell-1}(1-q^{j}x+\gamma\delta q^{2j+1})={{}_{4}\phi_{3}}\left({q^% {-n},\alpha\beta q^{n+1},q^{-y},\gamma\delta q^{y+1}\atop\alpha q,\beta\delta q% ,\gamma q};q,q\right),}}

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DLMF:18.28.E19

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Symbols defined

$$q$$ -Racah polynomial

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{\displaystyle{\displaystyle n=0,1,\dots,N}}

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basic hypergeometric (or $$q$$ -hypergeometric) function

Defining formula

{\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},% \dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}

C17.S4.E1.m2agdec

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Defining formula

{\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}% \right)_{\NVar{n}}}}

C17.S2.SS1.p1.m6agdec

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Defining formula

{\displaystyle{\displaystyle y}}

C18.S1.XMD1.m1bdec

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Defining formula

{\displaystyle{\displaystyle q}}

C18.S1.XMD3.m1pdec

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Defining formula

{\displaystyle{\displaystyle\ell}}

C18.S1.XMD4.m1fdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1ndec

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Defining formula

{\displaystyle{\displaystyle N}}

C18.S1.XMD7.m1dec

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Defining formula

{\displaystyle{\displaystyle\delta}}

C18.S1.XMD8.m1dec

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Defining formula

{\displaystyle{\displaystyle x}}

C18.S2.XMD3.m1hdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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